Related papers: A logifold structure on measure space

The structure of real-world networks is usually difficult to characterize owing to the variation of topological scales, the nondyadic complex interactions, and the fluctuations in the network. We aim to address these problems by introducing…

The production of thematic maps depicting land cover is one of the most common applications of remote sensing. To this end, several semantic segmentation approaches, based on deep learning, have been proposed in the literature, but land…

Few-shot dataset generalization is a challenging variant of the well-studied few-shot classification problem where a diverse training set of several datasets is given, for the purpose of training an adaptable model that can then learn…

Locally-biased graph algorithms are algorithms that attempt to find local or small-scale structure in a large data graph. In some cases, this can be accomplished by adding some sort of locality constraint and calling a traditional graph…

High-dimensional data analysis typically focuses on low-dimensional structure, often to aid interpretation and computational efficiency. Graphical models provide a powerful methodology for learning the conditional independence structure in…

We present the applications of methods from nonlinear local harmonic analysis for calculations in nonlinear collective dynamics described by different forms of Vlasov-Maxwell-Poisson equations. Our approach is based on methods provided the…

We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature. Our measure uses the framework of diffusion maps, including the data diffusion operator, to structure point cloud data and define local…

This study investigates the use of local optima network (LON) analysis, a derivative of the fitness landscape of candidate solutions, to characterise and visualise the neural architecture space. The search space of feedforward neural…

Log-linear models are a family of probability distributions which capture relationships between variables. They have been proven useful in a wide variety of fields such as epidemiology, economics and sociology. The interest in using these…

We present a domain decomposition strategy for developing structure-preserving finite element discretizations from data when exact governing equations are unknown. On subdomains, trainable Whitney form elements are used to identify…

The paper discuss the limit point concept of a subset in a group via ideal of the power set ring. This idea along with anti-ideal give the topological structure in a group. Homomorphic images of both ideal and anti-ideal are played the…

This paper presents an alternative approach of analyzing possibly multitype point patterns in space and space-time that occur on network structures, and introduces several different graph-related intensity measures. The proposed formalism…

We introduce a method called multi-scale local shape analysis, or MLSA, for extracting features that describe the local structure of points within a dataset. The method uses both geometric and topological features at multiple levels of…

Network is a simple but powerful representation of real-world complex systems. Network community analysis has become an invaluable tool to explore and reveal the internal organization of nodes. However, only a few methods were directly…

Large datasets represented by multidimensional data point clouds often possess non-trivial distributions with branching trajectories and excluded regions, with the recent single-cell transcriptomic studies of developing embryo being notable…

When network and graph theory are used in the study of complex systems, a typically finite set of nodes of the network under consideration is frequently either explicitly or implicitly considered representative of a much larger finite or…

Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…

Indoor localization using deep learning (DL) has demonstrated strong accuracy in mapping Wi-Fi RSS fingerprints to physical locations; however, most existing DL frameworks function as black-box models, offering limited insight into how…

This paper offers a new perspective to ease the challenge of domain generalization, which involves maintaining robust results even in unseen environments. Our design focuses on the decision-making process in the final classifier layer.…

Research in point cloud analysis with deep neural networks has made rapid progress in recent years. The pioneering work PointNet offered a direct analysis of point clouds. However, due to its architecture PointNet is not able to capture…